The self-tuning feedback controller (SFC) described in this paper is mathematically and structurally equivalent to a conventional, discrete, PID, feedback controller. However, it also includes a simple estimation or adaptive algorithm that tunes the controller constants such that a quadratic performance index with a control weighting term is minimized. Global stability is mathematically proven in the presence of bounded, external unmeasured inputs. Application of the SFC to a pilot-plant evaporator demonstrates the practicality of this algorithm.